Speed of light based oscillator frequency

ABSTRACT

An oscillator and a method of fabricating the oscillator are described. The oscillator includes a resonator with a plurality of transmission lines. An oscillation frequency of the oscillator is independent of at least one dimension of the plurality of transmission lines. The oscillator also includes a negative resistance circuit coupled to the resonator that cancels internal loss resistance of the resonator.

BACKGROUND

The present invention relates to a transmission line resonator, and more specifically, to a speed of light referenced frequency oscillator.

The generation of signals having frequencies with wavelengths on the order of millimeters (mm-waves) is challenged by the lack of low phase-noise oscillators that work at the carrier frequency and have a large tuning range. On-chip complementary metal-oxide-semiconductor (CMOS) variable capacitances (varactors) have low quality factors (Qs) (e.g., less than 10). As a result, a voltage-controlled oscillator (VCO) based on integrated varactors may have a high phase noise and a limited tuning range. Currently available high-Q on-chip resonators are not only bulky but also have no means to tune their frequency characteristics. Alternative devices use a phase-locked loop (PLL) working at lower frequencies and frequency multipliers (e.g., doublers, triplers) to generate a mm-wave carrier. These multiplying devices need active devices and passive devices such as inductor and capacitors. Moreover, these multipliers have poor efficiency. As a result, there is a power penalty and area penalty to generate the higher frequencies. In addition, the generated signals at mm-waves need amplifiers and buffers to drive the up/down conversion mixers.

SUMMARY

According to one embodiment of the present invention, an oscillator includes a resonator comprising a plurality of transmission lines, an oscillation frequency of the oscillator being independent of at least one dimension of the plurality of transmission lines; and a negative resistance circuit coupled to the resonator and configured to cancel internal loss resistance of the resonator.

According to another embodiment, a method of fabricating an oscillator includes arranging a plurality of transmission lines to form a resonator whose oscillation frequency is referenced to a speed of light and is independent of at least one dimension of the plurality of transmission lines; and coupling a negative resistance circuit to the resonator, the negative resistance circuit being configured to cancel internal loss resistance of the resonator.

Additional features and advantages are realized through the techniques of the present invention. Other embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed invention. For a better understanding of the invention with the advantages and the features, refer to the description and to the drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The forgoing and other features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which:

FIG. 1 illustrates a parallel plate transmission line according to an embodiment of the invention;

FIG. 2 shows a quarter lambda (λ/4) transformer and a capacitor, both comprising the parallel plate transmission lines according to an embodiment of the invention;

FIG. 3 shows a transmission line resonator according to an embodiment of the invention;

FIG. 4 illustrates exemplary arrangements of the transmission lines of the resonator according to embodiments of the invention;

FIG. 5 depicts a fixed frequency oscillator according to an embodiment of the invention;

FIG. 6 illustrates exemplary oscillators according to different embodiments of the invention;

FIG. 7 depicts a variable frequency transmission line resonator including tunable capacitors according to an embodiment of the invention;

FIG. 8 illustrates exemplary oscillators including tunable capacitors according to embodiments of the invention;

FIG. 9 depicts a variable frequency transmission line resonator including tunable inductors according to an embodiment of the invention;

FIG. 10 illustrates exemplary oscillators including tunable inductors according to embodiments of the invention;

FIG. 11 shows quadrature oscillators according to embodiments of the invention;

FIG. 12 is a block diagram of an on-off keying receiver including the oscillator according to embodiments of the invention;

FIG. 13 is a block diagram of radios that include an oscillator according to an embodiment of the invention;

FIG. 14 is a block diagram of a mm-wave digital phase locked loop (PLL) that includes an oscillator according to an embodiment of the invention;

FIG. 15 is a block diagram of oscillators according to an embodiment of the invention that may be used in a terahertz (THz) source; and

FIG. 16 is a process flow of a method of fabricating an oscillator according to embodiments described herein.

DETAILED DESCRIPTION

As noted above, oscillators that generate mm-wave frequency signals suffer from issues of phase noise and tuning range. Typically, a VCO includes a resonator in which a capacitor and inductor resonate to give the frequency of oscillation when provided with energy. Sources of inaccuracy can change the oscillation frequency. One source of inaccuracy is an inconsistency in the dimensions of the capacitor and inductor in the manufacturing. Embodiments of the resonator described herein provide a frequency of oscillation that is referenced to the speed of light and is independent of at least one dimension and up to two dimensions.

FIG. 1 illustrates a parallel plate transmission line 100 according to an embodiment of the invention. The transmission line 100 shown in FIG. 1 is a building block of the resonator 300 (see e.g., FIG. 3) according to embodiments of the invention. The transmission line 100 includes two metal plates 110 a, 110 b arranged in parallel with a dielectric material 120 separating them. The dimensions of the transmission line 100 are given by a length (l), width (w), and depth of the dielectric material 120 (d) which is the distance of separation between the two metal plates 110 a, 110 b. The resistance of the transmission line 100 (R_(Line)) is given by:

$\begin{matrix} {R_{Line} = \frac{2}{w*\sigma_{cond}*\delta}} & \left\lbrack {{EQ}.\mspace{14mu} 1} \right\rbrack \end{matrix}$ where w is the width of the transmission line metal plates 110 a and 110 b as shown in FIG. 1, σ_(cond) is the conductance of the metal plates 110 a, 110 b, and δ is the skin effect, which is given by:

$\begin{matrix} {\delta = \sqrt{\frac{2}{\omega*\mu*\sigma_{cond}}}} & \left\lbrack {{EQ}.\mspace{14mu} 2} \right\rbrack \end{matrix}$ where ω is the frequency of the transmission line 100 in radians and μ is the permeability. The inductance per unit length of the transmission line 100 (L_(Line)) is given by:

$\begin{matrix} {L_{Line} = {\mu_{0}*\mu_{r}*{\frac{d}{w}\left\lbrack \frac{Henry}{meter} \right\rbrack}}} & \left\lbrack {{EQ}.\mspace{14mu} 3} \right\rbrack \end{matrix}$ Where d is the distance between the transmission line metal plates 110 a and 110 b as shown in FIG. 1, μ₀ to (permeability in a vacuum) and μ_(r) (relative permeability of the transmission line 100 with respect to μ₀) are the total permeability (μ). As EQ. 3 indicates, the inductance decreases as the width of the transmission line metal plates 110 a and 110 b increases. The capacitance per unit length of the transmission line 100 (C_(Line)) is given by:

$\begin{matrix} {C_{Line} = {ɛ_{0}*ɛ_{r}*{\frac{w}{d}\left\lbrack \frac{Farad}{meter} \right\rbrack}}} & \left\lbrack {{EQ}.\mspace{14mu} 4} \right\rbrack \end{matrix}$ where ε₀*ε_(r) is the total dielectric constant. As EQ. 4 indicates, the capacitance increases as the width of the transmission line metal plates 110 a and 110 b increases. That is, although FIGS. 2, 3, and 5-8 show capacitors, alternate embodiments of the invention include transmission lines 100 forming inductors (see e.g., FIGS. 9 and 10) based on the width of the transmission line metal plates 110 a and 110 b that make up the transmission lines 100. The conductance per unit length of the transmission line 100 (G_(Line)) is given by:

$\begin{matrix} {G_{Line} = {\sigma_{cond}*{\frac{w}{d}\left\lbrack \frac{Siemens}{meter} \right\rbrack}}} & \left\lbrack {{EQ}.\mspace{14mu} 5} \right\rbrack \end{matrix}$

FIG. 2 shows a quarter lambda (λ/4) transformer 200 and a capacitor C 220, both comprising the parallel plate transmission lines 100 according to an embodiment of the invention. The quarter lambda transformer 200 forms the inductor of the resonator 300 (see e.g., FIG. 3). As shown in FIG. 2, the quarter lambda transformer 200 comprises three transmission lines 100 as shown and discussed with reference to FIG. 1, the metal plate 110 a of each being visible in FIG. 2. The width (w) and depth (d) of each of the transmission lines 100 shown in FIG. 2 are assumed to be the same. The length (l) of the waveguides 210 is a quarter of the wavelength corresponding to the transmission frequency, and the length of capacitor C 220 is given by lcap (capacitor C 220 and the corresponding capacitance C are both references with C). The input impedance (230) Z_(in) is given by:

$\begin{matrix} {Z_{in} = {\frac{Z_{0}^{2}}{Z_{C}} = {{{j\omega}\; C*Z_{0}^{2}} = {{j\omega}\; L}}}} & \left\lbrack {{EQ}.\mspace{14mu} 6} \right\rbrack \end{matrix}$ where the impedance of the waveguides 210 is Z₀, the load or capacitor 220 impedance is Z_(C), C is the capacitance, and L is the inductance. As a result, using EQ. 6, the inductance L is given by: L=Z ₀ ² *C  [EQ. 7] According to EQ. 4, which provides the capacitance per unit length, the capacitance C may also be written as:

$\begin{matrix} {C = {ɛ_{0}*ɛ_{r}*\frac{w}{d}*l}} & \left\lbrack {{EQ}.\mspace{14mu} 8} \right\rbrack \end{matrix}$ In addition, the impedance of the waveguides 210 is given by:

$\begin{matrix} {Z_{0} = {\frac{d}{w}*\sqrt{\frac{\mu_{0}*\mu_{r}}{ɛ_{0}*ɛ_{r}}}}} & \left\lbrack {{EQ}.\mspace{14mu} 9} \right\rbrack \end{matrix}$ By substituting the capacitor C 220 capacitance (C) from EQ. 8 and the waveguide 210 inductance (Z₀) from EQ. 9 into EQ. 7, the inductance of the quarter lambda transformer 200 may be determined as:

$\begin{matrix} {L = {\mu_{0}*\mu_{r}*\frac{d*l}{w}}} & \left\lbrack {{EQ}.\mspace{14mu} 10} \right\rbrack \end{matrix}$

FIG. 3 shows a transmission line resonator 300 according to an embodiment of the invention. The resonator 300 includes the quarter lambda transformer 200 shown in FIG. 2, which acts as the inductor of the resonator 300 with inductance indicated by EQ. 10. The resonator 300 also includes the capacitor C₁ 310, which acts as the capacitor of the resonator 300 with a capacitance given by:

$\begin{matrix} {C_{1} = {ɛ_{0}*ɛ_{r}*\frac{w}{d}*l_{1}}} & \left\lbrack {{EQ}.\mspace{14mu} 11} \right\rbrack \end{matrix}$ where l₁ is the length of the capacitor C₁ 310. With the inductance (L) given by EQ. 10 and capacitance (C₁) given by EQ. 11, the oscillation frequency (f_(osc)) of the resonator 300 in Hertz (Hz) is:

$\begin{matrix} {f_{osc} = {\frac{1}{2\pi\sqrt{{LC}_{1}}} = {\frac{1}{2\pi\sqrt{l*l\; 1}}*\frac{c}{\sqrt{ɛ_{r}*\mu_{r}}}}}} & \left\lbrack {{EQ}.\mspace{14mu} 12} \right\rbrack \end{matrix}$ where the speed of light (c) is given by:

$\begin{matrix} {c = \frac{1}{\sqrt{ɛ_{0}*\mu_{0}}}} & \left\lbrack {{EQ}.\mspace{14mu} 13} \right\rbrack \end{matrix}$ As EQ. 12 illustrates, the frequency of oscillation of the resonator 300 is referenced to the speed of light (c) and is independent of the width and depth of the transmission lines 100 that make up the resonator 300. Instead, the oscillation frequency depends on the lengths (l and l₁) corresponding with the capacitors C 220 and C₁ 310 and the material properties (ε_(r) and μ_(r)) of the metal plates 110 a of the transmission lines 100. The precision with which the oscillation frequency is attained depends on the precision of the mask involved in the processing of the integrated circuit. The precision of the oscillation frequency is represented by a variation (Δf_(osc)) in the frequency of oscillation and is given by:

$\begin{matrix} {\frac{\Delta\; f_{osc}}{f_{osc}} = {{- \frac{1}{2}}\left( {\frac{\Delta\; l}{l} + \frac{\Delta\; l_{1}}{l_{1}}} \right)}} & \left\lbrack {{EQ}.\mspace{14mu} 14} \right\rbrack \end{matrix}$

FIG. 4 illustrates exemplary arrangements of the transmission lines 100 of the resonator 300 according to embodiments of the invention. The length of the waveguides 210 are always a quarter of the wavelength corresponding with the oscillation frequency. However, that length (λ/4) may be implemented in a stepped fashion in some embodiments and as a straight line in other embodiments, as shown in FIG. 4. The overall length of the waveguides 210 according to any of the arrangements is a quarter of the wavelength corresponding with the oscillation frequency (the inductor of the resonator 300 is implemented as a quarter lambda transformer) and the oscillation frequency of the resonator 300 depends only on the lengths (l and l₁) of the capacitors C 220 and C₁ 310, respectively.

FIG. 5 depicts a fixed frequency oscillator 500 according to an embodiment of the invention. The oscillator 500 includes the resonator 300 comprised of the transmission lines 100 and a negative resistance 510 (−R_(N)). The negative resistance 510 (−R_(N)) essentially creates a resonator 300 with no damping and can be thought of as adding energy to the system. If the oscillation loss of the resonator 300 were modeled as a resistance (R), then the negative resistance 510 (−R_(N)) cancels out the resistance (R). FIG. 6 illustrates exemplary fixed frequency oscillators 500 according to different embodiments of the invention. FIG. 6 shows three different exemplary topologies of the oscillator 500 with three different implementations of the negative resistance 510 (−R_(N)). Each of the exemplary topologies of the oscillator 500 also includes the application of a bias voltage resulting in the bias current 610. The oscillators 500 may be used in CMOS or bipolar transistor applications.

FIG. 7 depicts a variable frequency transmission line 100 resonator 700 including tunable capacitors (C 710 and C₁ 720) according to an embodiment of the invention. Like the resonator 300 shown in FIG. 3, the resonator 700 of FIG. 7 is implemented using transmission lines 100. However, unlike the fixed-frequency resonator 300, the resonator 700 has a tunable oscillation frequency as discussed below. The capacitors (C 710 and C₁ 720) of the resonator 700 may be implemented as variable capacitors with variable lengths (l₇ and l₇₋₁, respectively). Because the oscillation frequency depends on the lengths (l₇ and l₇₋₁) of the capacitors (C 710 and C₁ 720) as shown in EQ. 12, the oscillation frequency varies as the lengths (l₇ and l₇₋₁) vary. As shown in FIG. 7, exemplary lengths (l₇) for the transmission line 100 making up the capacitor C 710 of the quarter lambda transformer (inductor of the resonator 700) may be within a range d₀ through d₅ with any number of incremental values in between. Exemplary lengths (l₇₋₁) for the transmission line 100 making up the capacitor C₁ 720 of the resonator 700 may be within a range b₀ through b₅. One or both of the lengths (l₇ and l₇₋₁) may be changed at one time to adjust the oscillator frequency. The capacitors (C 710 and C₁ 720) may be tuned digitally. By tuning one or both of the capacitors (C 710 and C₁ 720), the resonator 700 may be implemented as a tunable resonator with two independent tuning inputs. FIG. 8 illustrates exemplary oscillators 800 including tunable capacitors according to embodiments of the invention. The three different exemplary topologies of the oscillators 800 shown in FIG. 8 include tunable capacitors (C 220 and C₁ 310) such that the oscillators 800 have tunable oscillation frequencies. FIG. 8 shows three different exemplary implementations of the negative resistance 510 (−R_(N)). The three implementations of the negative resistance 510 (−R_(N)) shown in FIG. 8 for the tunable oscillation frequency oscillators 800 are the same as those shown in FIG. 6 for the fixed oscillation frequency oscillators 500.

FIG. 9 depicts a variable frequency transmission line 100 resonator 900 including tunable inductors (L 910 and L₁ 920) according to an embodiment of the invention. The resonator 900 includes inductors L 910 and L₁ 920 that have respective tunable lengths l₉ and l₉₋₁. The relationship between inductance of the inductor L 910 and capacitance is given by EQ. 7 above and depends on the impedance Z₀ of the transmission lines 100 making up the waveguides 210. The length (l₉ and l₉₋₁) of the inductors (L 910 and L₁ 920) may be adjusted individually or collectively to adjust the oscillation frequency of the resonator 900. While the same ranges (d₀ through d₅ and b₀ through b₅) of adjustment are shown for the lengths l₉ and l₉₋₁ of the inductors L 910 and L₁ 920, respectively, as are shown for the lengths l₇ and l₇₋₁ of the adjustable capacitors C 710 and C₁ 720 shown in FIGS. 7 and 8, the ranges need not be the same. As with the resonator shown in FIG. 7, the resonator 900 of FIG. 9 is tunable with two independent inputs (i.e., inductor L 910 and L₁ 920 lengths l₉ and l₉₋₁). FIG. 10 illustrates exemplary oscillators 1000 including tunable inductors (L 910 and L₁ 920) according to embodiments of the invention. The three different exemplary topologies of the oscillators 1000 shown in FIG. 10 include tunable inductors (L 910 and L₁ 920) such that the oscillators 1000 have tunable oscillation frequencies. FIG. 10 shows three different exemplary implementations of the negative resistance 510 (−R_(N)). The three implementations of the negative resistance 510 (−R_(N)) shown in FIG. 10 for the tunable oscillation frequency oscillators 1000 are the same as those shown in FIG. 6 (for the fixed oscillation frequency oscillators 500) and FIG. 8 (for the tunable oscillation frequency oscillators 700).

FIG. 11 shows quadrature oscillators 1110, 1120 according to embodiments of the invention. Each of the quadrature oscillators 1110, 1120 has a symmetric structure with an exemplary implementation of the negative resistance 510 (−R_(N)) on each side of the resonator 1105, 1115. As a result of the symmetrical arrangement, two output oscillation frequencies, with a 90 degree phase difference between them, are obtained from each of the quadrature oscillators 1110, 1120. The resonators 1105, 1115 include the waveguides 210. The other two transmission lines 100 (1130, 1140) may be capacitors (220, 310), as discussed with reference to FIG. 3, tunable capacitors (710, 720), as discussed with reference to FIG. 7, or tunable inductors (910, 920), as discussed with reference to FIG. 9. The resonators 1105, 1115 may be fabricated according to any of the embodiments discussed above. As such, the resonators 1105, 1115 have a quadrature oscillation frequency that is referenced to the speed of light and is independent of with width (w) and depth (d) of the transmission lines 100 that comprise the resonators 1105, 1115 (see e.g., EQ. 12). Each of the resonators 1105, 1115 shows biasing, through quarter wavelength lines 1150, of the transmission lines 1130, 1140 (in resonator 1106) or the waveguides 210 (in resonator 1115).

The various embodiments of the fixed frequency and variable frequency oscillators (500, 800, 1000, 1110, 1120) discussed above may be used in any application requiring an oscillator. For example, FIG. 12 is a block diagram of an on-off keying (OOK) receiver 1200 including the oscillator (500, 800, 1000) according to embodiments of the invention. In the OOK receiver 1200 according to one embodiment, the oscillator 500 may provide the quench signal. The oscillator 500 in this application may be generated with an on-chip reference based on a fixed resonator voltage controlled oscillator without an external crystal oscillator. The accuracy of the oscillator 500 frequency (quench frequency) may be precise within the mask accuracy and is acceptable as long as the frequency is greater than a multiple (e.g., 60 times) the receiver input frequency. The tunable oscillators (800, 1000) may also be used in this application. As another example, FIG. 13 is a block diagram of radios 1300 that include an oscillator 800 according to an embodiment of the invention. The oscillator 800 may be used as a reference for crystal-less radios 1300. As FIG. 13 illustrates, the slave device 1310 has no crystal (like the crystal 1320 of the master device 1330). The OOK receiver 1340 is always on. If a beacon from the master device 1330 is present, the phase locked loop (PLL) 1350 switches to the external reference (f_(REF)) from the OOK receiver 1340. Without the beacon from the master device 1330, the PLL 1350 takes the reference from the on-chip oscillator 800. The slave device 1310 locks to the master device 1330 immediately because the PLL 1350 acquires reference frequency (f_(REF)) information from the beacon and the difference between f_(REF) and f_(RES) (the frequency from the oscillator 800) is very small. Thus, the pull-in time for the PLL 1350 (to switch from f_(RES) to f_(REF) is very small). FIG. 14 is a block diagram of a millimeter wave (mm-wave) digital PLL 1400 that includes an oscillator 800 according to an embodiment of the invention. The up/down converter 1410 detects the sign of the time-to-digital converter (TDC) 1420. The divider 1430 works at mm-waves and may be realized with resonant loads. As yet another example, FIG. 15 is a block diagram of oscillators 1000 according to an embodiment of the invention that may be used in a THz source 1500.

FIG. 16 is a process flow of a method of fabricating an oscillator (500, 800, 1000, 1110, 1120) according to embodiments described herein. At block 1610, arranging transmission lines 100 to form a resonator (300, 700, 900, 1105, 1115) may be according to the various embodiments described above. The transmission lines 100 used as waveguides 210 may be combined with a fixed-length capacitor (C 220) or variable-length capacitor (C 710) or variable-length inductor (L 910) and the resonator additionally includes a fixed-length capacitor (C₁ 310) or variable-length capacitor (C₁ 720) or variable-length inductor (L₁ 920). At block 1620, adjusting the length to tune the frequency of oscillation includes adjusting the capacitor (C 220, 710) or inductor (L 710), adjusting the capacitor (C₁ 310, 720) or inductor (L₁ 920), or both as discussed with reference to FIGS. 7 and 9. At block 1630, arranging one or more energy sources (negative resistance 510) for the resonator (300, 700, 900, 1105, 1115) arranged according to blocks 1610 and, optionally, 1620 may include providing a single energy source to obtain an oscillator (500, 800, 1000) or two symmetric energy sources to obtain a quadratic oscillator (1110, 1120).

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one more other features, integers, steps, operations, element components, and/or groups thereof.

The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated

The flow diagram depicted herein is just one example. There may be many variations to this diagram or the steps (or operations) described therein without departing from the spirit of the invention. For instance, the steps may be performed in a differing order or steps may be added, deleted or modified. All of these variations are considered a part of the claimed invention.

While the preferred embodiment to the invention had been described, it will be understood that those skilled in the art, both now and in the future, may make various improvements and enhancements which fall within the scope of the claims which follow. These claims should be construed to maintain the proper protection for the invention first described. 

What is claimed is:
 1. An oscillator, comprising: a resonator comprising a plurality of transmission lines, an oscillation frequency of the oscillator being independent of at least one dimension of the plurality of transmission lines; and a negative resistance circuit coupled to the resonator and configured to cancel internal loss resistance of the resonator, wherein the resonator comprises four transmission lines and a first transmission line and a second transmission line of the four transmission lines have a respective first length and second length of one-fourth of a wavelength corresponding with the oscillation frequency.
 2. The oscillator according to claim 1, wherein the resonator outputs a signal whose oscillation frequency is a function of the speed of light.
 3. The oscillator according to claim 1, wherein the oscillation frequency is independent of a width and depth of the plurality of transmission lines.
 4. The oscillator according to claim 1, wherein a third transmission line of the four transmission lines has a third length and the third length is different than the first length and the second length.
 5. The oscillator according to claim 1, wherein a third transmission line of the four transmission lines has a third length and the third length is a same length as the first length and the second length.
 6. The oscillator according to claim 1, wherein a third transmission line of the four transmission lines has a tunable third length and a change in the third length causes a corresponding change in the oscillation frequency.
 7. The oscillator according to claim 6, wherein a fourth transmission line of the four transmission lines has a tunable fourth length and a change in the fourth length causes a corresponding change in the oscillation frequency.
 8. The oscillator according to claim 1, further comprising a second negative resistance circuit coupled to the resonator, the negative resistance circuit and the second negative resistance circuit being arranged symmetrically with respect to the resonator.
 9. The oscillator according to claim 8, wherein the oscillator is a quadrature oscillator configured to provide two output signals having a same frequency that are 90 degrees out of phase with each other. 